An oath is administered in a cathedral to pledge support for a governor. This is an indicator of the role of religion in politics in societies of the late 19th century.

Page 696.
" After dinner things become gayer still. The governor invited Vronsky to a concert in aid of ‘Our Serbian brothers’ which was being organized by his wife, who wished to make Vronsky’s acquaintance. "

This refers to the political turmoil in Serbia in the 1860s that culminated in clashes between the Ottomans and Serbian civilians in 1862. It was the second state in Eastern Europe to abolish serfdom and feudalism.

Streptococcus pneumoniae, one of the bacteria responsible for pneumonia

Anna's daughter has pneumonia. This is an infection caused by either bacteria, fungi, or protozoa associated with cold which may further point to her poor ability as a mother. Pneumonia was a major killer disease around the time described in the novel before scientific advancement later contained it in Europe. It remains dangerous in third world countries but its prevalence has been reduced to manageable levels.